Expand: `(x-(1)/(x)+5)^(2)`

Answer

To expand the expression \((x - \frac{1}{x} + 5)^{2}\), we can use the formula for the square of a trinomial, which is:

\[ (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca \]

### Step-by-step Solution:

1. **Identify the terms**:
Let \( a = x \), \( b = -\frac{1}{x} \), and \( c = 5 \).

2. **Calculate \( a^{2} \)**:
\[ a^{2} = x^{2} \]

3. **Calculate \( b^{2} \)**:
\[ b^{2} = \left(-\frac{1}{x}\right)^{2} = \frac{1}{x^{2}} \]

4. **Calculate \( c^{2} \)**:
\[ c^{2} = 5^{2} = 25 \]

5. **Calculate \( 2ab \)**:
\[ 2ab = 2 \cdot x \cdot \left(-\frac{1}{x}\right) = -2 \]

6. **Calculate \( 2bc \)**:
\[ 2bc = 2 \cdot \left(-\frac{1}{x}\right) \cdot 5 = -\frac{10}{x} \]

7. **Calculate \( 2ca \)**:
\[ 2ca = 2 \cdot 5 \cdot x = 10x \]

8. **Combine all the terms**:
Now, we can combine all the calculated parts:
\[ (x - \frac{1}{x} + 5)^{2} = x^{2} + \frac{1}{x^{2}} + 25 - 2 - \frac{10}{x} + 10x \]

9. **Simplify the expression**:
\[ = x^{2} + \frac{1}{x^{2}} + 23 - \frac{10}{x} + 10x \]

### Final Result:
Thus, the expanded form of \((x - \frac{1}{x} + 5)^{2}\) is:
\[ x^{2} + \frac{1}{x^{2}} + 23 - \frac{10}{x} + 10x \]